What is a Functor? Definition and Examples, Part 1

Next up in our mini series on basic category theory: functors! We began this series by asking What is category theory, anyway? and last week walked through the precise definition of a category along with some examples. As we saw in example #3 in that post, a functor can be viewed an arrow/morphism between two categories.

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Introducing... crumbs!

Hello friends! I've decided to launch a new series on the blog called crumbs! Every now and then, I'd like to share little stories -- crumbs, if you will -- from behind the scenes of Math3ma. To start us off, I posted (a slightly modified version of) the story below on January 23 on Facebook/Twitter/Instagram, so you may have seen this one already. Even so, I thought it'd be a good fit for the blog as well. I have a few more of these quick, soft-topic blurbs that I plan to share throughout the year. So stay tuned! I do hope you'll enjoy this newest addition to Math3ma.

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What is a Category? Definition and Examples

As promised, here is the first in our triad of posts on basic category theory definitions: categories, functors, and natural transformations. If you're just now tuning in and are wondering what is category theory, anyway? be sure to follow the link to find out!

A category $\mathsf{C}$ consists of some data that satisfy certain properties...

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What is Category Theory Anyway?

A quick browse through my Twitter or Instagram accounts, and you might guess that I've had category theory on my mind. You'd be right, too! So I have a few category-theory themed posts lined up for this semester, and to start off, I'd like to (attempt to) answer the question, What is category theory, anyway? for anyone who may not be familiar with the subject.

Now rather than give you a list of definitions--which are easy enough to find and may feel a bit unmotivated at first--I thought it would be nice to tell you what category theory is in the grand scheme of (mathematical) things. You see, it's very different than other branches of math....

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If you've been following this blog for a while, you'll know that I have strong opinions about the misconception that "math is only for the gifted." I've written about the importance of endurance and hard work several times. Naturally, these convictions carried over into my own classroom this past semester as I taught a group of college algebra students.

Whether they raised their hand during a lecture and gave a "wrong" answer, received a less-than-perfect score on an exam or quiz, or felt completely confused during a lesson, I tried to emphasize that things aren't always as bad as they seem...

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